de Broglie wavelength for a particle is given by
λ==, where
m,v and
p are the mass, velocity and momentum respectively.
h is Planck's constant. Now, since all the particles are moving with same velocity, the particle with least mass will have maximum de-Broglie wavelength. Out of the given four particles (proton, neutron,
α -particles, i.e., He nucleus and
β -particles, i.e., electrons)
β -particle has the lowest mass and therefore it has maximum wavelength.